A generalized method for Sparse Partial Least Squares (Dual-SPLS): theory and applications

In data analysis, high dimensionality is often a delicate obstacle to overcome which can be solved by representing the data in a lower dimensional space using projection methods like the Partial Least Squares regression (PLS) or by resorting to variable selection methods like the lasso approach. The Sparse Partial Least Squares (SPLS) combines the two latter in order to better interpret the results due to the sparsity imposed on the new directions. Several implementations have been proposed. However, problems of accuracy of predictions and correct interpretation of regression coefficients arise in these approaches. Hence we developed the Dual Sparse Partial Least Squares, a flexible method that results in more accurate predictions and better interpre- tation of the coefficients due to their sparsity. In this paper we present the theory behind Dual-SPLS and some applicative results on petroleum data sets.